I think that postmodernist music is more self-conscious about its relationship to tradition than modernism. An archetypical postmodern piece would be something like Berio's Sinfonia, with its layers of historical strata. It is not merely
within tradition, as say, Schoenberg's Piano Concerto with its waltzes or Stravinsky's Octet with its non-functional treatment of Baroque formulae, it comments on tradition by the way it openly selects and contextualizes its materials.
https://www.youtube.com/v/V1XSmiGO3XEFew works so actively embody a postmodern aesthetic though. I think in general there was a trend moving away from the linguistic consistency of a Stravinsky or a Schoenberg to the variety of a Berio or Rochberg, but at the same time you can find composers like Elliott Carter or Pierre Boulez who made their life projects in forging a consistent personal language. The later 20th century was, like the early 20th century, a time of great musical diversity.